recourse to Pythagoras to
explain it; in this rule, as in others, _e.g._ their taboo on eating
beans, the Pythagoreans were only following a native prejudice of
southern Italy. "The idea of luck in odd numbers," says Mr. Crooke,[197]
writing of the Hindus, "is universal." Thus the simpler odd numbers,
three, five, seven, and nine, all recur constantly in folklore; and the
result is visible in this calendar. Where a festival occupies more than
one day in a month, there is an interval between the two of one or three
days, making the whole number three or five. Thus Carmentalia occur on
11th and 15th January, and the Lemuria in May are on the 9th, 11th, and
13th; the Lucaria in July on 19th and 21st. In some months, too, _e.g._
August and December, perhaps also July and February, there seem to be
traces of an arrangement by which festivals which probably had some
connection with each other are thus arranged; _e.g._ in August six
festivals, all concerned in some way with the fruits of the earth and
the harvest, occur on the 17th, 19th, 21st, 23rd, 25th, and 27th. It has
recently been suggested[198] that these are arranged round one central
festival, which gives a kind of colouring to the others, as the
Volcanalia in August, the Saturnalia in December. But the reasons von
Domaszewski gives for the arrangement, and the further speculation that
where it does not occur we may find traces of an older system, as yet
unaffected by the so-called Pythagorean prejudice, do not seem to me
satisfactory. We may be content with the general principle as I have
stated it, and note that while religious duties _must_ be performed on
days of odd number, civil duties were not so restricted: the days
belonging to the gods, which were, so to speak, taboo days, were more
important than those belonging to men. There are, as I have said, but
two days marked in the large letters as festivals, which are on days of
even number, 24th February and 14th March, the Regifugium and the second
Equirria; and about these we know so little that it is almost useless to
speculate as to the reason for their exception from the rule. Two
others, 24th March and 24th May, were partly the property of the gods
and partly of men, and are marked QRCF (_quando rex comitiavit fas_);
but the sense in which they partially belonged to the gods is not the
same as in the case of sacrificial festivals.

This calendar thus shows obvious signs of both military and political
develo